Article and a method for producing an article having a high friction surface

ABSTRACT

Improved abrasive tools and apparatus and method for the manufacture of the improved abrasive tools and the like which includes apparatus and a method for the creation of a structurally viable matrix having a pattern of abrasive elements which can be shaped, cut and positioned for permanent disposition on a rigid tool body. The apparatus includes a release layer on a transversely magnetized base surface with magnetic protrusions to provide a mosaic-like surface. Magnetizable abrasive particles applied to the release layer orient themselves magnetically to form generally conic stacks which having a stack axis and a distal working portion. The stacks define a working surface which is then coated. Prior to solidification of the coating the cones may be shaped or raked magnetically. A braze paste is applied to encapsulate the cones and form a flexible support web between the cones. The entire matrix may then be removed from the release surface and cut, shaped, aligned and formed to any desired shape or configuration. The resulting configurations can emphasize cutting speed, finish and/or versatility at optimum cost.

This application is a continuation pursuant to 3 CFR 1.53(b) ofapplication U.S. Ser. No. 08/862,526, filed May 23, 1997, now U.S. Pat.No. 5,891,204, a continuation of application U.S. Ser. No. 08/481,235filed Jun. 7, 1995, now abandoned; a division of application U.S. Ser.No. 08/066,491, filed May 24, 1993 now U.S. Pat. No. 5,578,099; adivision of application U.S. Ser. No. 07/937,238 filed Aug. 28, 1992,now U.S. Pat. No. 5,213,590; a continuation-in-part of application U.S.Ser. No. 07/453,684 filed Dec. 20, 1989 now U.S. Pat. No. 5,181,939.

FIELD OF THE INVENTION

This invention relates to high friction surfaces for use in abrasiveapplications and the preparation of such high friction surfaces. Inparticular, the present invention relates to abrasive tools prepared byuse of a matrix of braze paste and abrasive particles which have beenprepared on a fixture.

DESCRIPTION OF THE PRIOR ART

U.S. Pat. No. 3,913,217, hereinafter referred to as Oliver I, disclosesan abrasive tool comprising a tool blank having small steel ballssecured thereto which have been armed with magnetically oriented carbideparticles. The carbide particles are secured together and to the ballsby a braze alloy. An Oliver I type tool is typically prepared, in part,by first securing a single layer of small steel balls to the surface ofa tool blank. A magnet is then secured to the tool blank below theballs. Next magnetizable carbide particles are sprinkled onto the smallsteel balls. The magnetic flux concentrations produced by the flux pathpassing through the small steel balls cause carbide particles to collecton the outermost portions of the balls to form conical structures. Abraze paste consisting of a binder and a braze alloy is then applied toencapsulate all of the elements of the assembly. Finally, the entireassembly is subjected to heating in a brazing furnace which bonds thebraze alloy, the magnetizable particles and the balls into a unifiedstructure. When the assembly has cooled, it may be used as an abrasivetool.

Thus, Oliver I discloses an IN-SITU technique for preparing an abrasivetool which requires placement of permanent tool protrusions on theexternal surface of a tool blank. These tool protrusions are thenecessary surface for the magnetic formation of the conical structuresof particles on the tool. The protrusions may take the form of smallsteel balls (as described in the '217 patent) or shapes formed bymachining a profile in the external surface of the tool blank. In eithercase, the tool blank which is the foundation of the ultimate productmust be covered with protrusions. The small steel balls or otherprotrusions are an added material cost and require additional labor toapply. If the protrusions are produced by machining a profile in theexternal surface of the tool blank, substantial skill and specializedequipment must be used.

Further, the carbide particles form structures which align with themagnetic flux emanating from the magnetized tool blank. In the case of acylindrical structure, the cones align with magnetic flux emanatingradially from the circumferential portion of the wheel. The conicalstructures formed thereby will be symmetrical in all respects, and whenused as a cutting tool will offer a negative rake angle to theworkpiece. The Oliver I technique is capable of producing only thesesymmetrical conical structures. If more aggressive rake angles orselectively oriented conical structures are desired, the Oliver Itechnique is not appropriate.

Finally, as with any cutting or abrading tool, heat produced duringcutting and abrading is conducted from the point of contact between thetool and the workpiece into the structure of the tool. When using anOliver I type tool, heat passes from the conical structures throughsmall steel balls and into the tool blank. Since these balls are brazedto the tool blank, they offer little more than point contact andconsequently present a substantial impediment to the flow of heat.

U.S. Pat. No. 4,916,869 hereinafter referred to as Oliver II, alsodiscloses an abrasive grit structure comprising a plurality of peakedportions. However in Oliver II each peak has an apex including anabrasive grit particle which is surrounded by setting material thatforms a substrate layer on which the peak portions are secured toprovide an integral structure. In a first embodiment, the peakedportions are formed by using a mold having a plurality of concaveindentations each of which receives an abrasive grit particle that isthen surrounded by setting material to establish an integral structure.The setting material may contain additional abrasive particles. A secondembodiment discloses a technique for molding using a mold having aplurality of concave indentations which are filled with abrasive gritparticles that are then transposed to a substrate surface as individualabrasive elements. Such a concept and structure is similarly describedin Woodell, et al. U.S. Pat. No. 2,001,911, Marvin U.S. Pat. No.2,793,427, Heck U.S. Pat. No. 3,431,105 and Bellinger U.S. Pat. No.3,102,011. In a third embodiment, a monolayer of abrasive particles aredistributed on a flat planar surface and structurally interconnected bya first layer of resin saturated braze alloy and a second layer of resinsaturated setting material. In the first and second embodiment, a brazealloy paste is applied to the abrasive grit structure after thestructure has been applied to a tool surface (i.e., IN-SITU). In thethird embodiment the braze alloy may be applied before the abrasivestructures are applied to the ultimate tool (NON IN-SITU). Upon heatingto braze conditions, the braze alloy infiltrates the abrasive gritstructure and bonds the abrasive particles and setting materials to thetool surface.

OBJECT OF THIS INVENTION

Accordingly, it is an object of this invention to provide an abrasivetool which reduces the time of preparation, labor and material costassociated with placement of a pattern of protrusions on a base toolstructure.

It is a specific object of this invention to provide an abrasive toolwith abrasive particle structures directly secured to the base toolstructure to improve the heat conduction away from the abrasive particlestructures.

It is another object of this invention to provide an abrasive tool withabrasive particle structures selectively offering negative, neutral orpositive rake angle cutting points to the workpiece.

It is another object of this invention to provide a matrix which may beincorporated in a process for manufacturing an abrasive tool which meetsthe aforestated objects and which minimizes the expense of manufacture.

It is another object of the present invention to provide a preferentialarrangement of abrasive elements to accomplish a range of performancegoals.

It is another object of this invention to provide a means tointerconnect the abrasive grit particles with a flexible structure andconjunctively provide adequate support for the abrasive grit particlesafter installation on the tool surface.

It is another object of the present invention to provide a matrix whichmay be prepared independently of a tool base and subsequently madeintegral with a tool form.

Other objects, advantages and features of the present invention willbecome apparent upon reading the following detailed description ofpreferred embodiments and the appended claims and upon reference to theaccompanying drawings.

SUMMARY OF THE PRESENT INVENTION

In accordance with one embodiment of the invention which achieves theforegoing objects, a fixture includes a generally planar magnetized basesurface with protrusions formed thereon to form a dotted or patchwork ormosaic surface. The protrusions may be machined into the surface orapplied to the surface in the form of small steel balls or otherdiscreet elements. A release mechanism or covering layer is then placedover the surface of the protrusions. The release mechanism may take theform of, for example, a thin coating of silicone or a thin sheet ofpolymeric material (such as Teflon). These parts form a fixture forrepetitive production of matrices.

Magnetizable abrasive particles are diffused or sprinkled onto thesurface of the release mechanism. The particles collect or orientthemselves along the lines of magnetic flux to form stacks, cones orelements having generally triangular cross sections. The distal portionsof the stacks have an element axis and a distal portion or workingportion. The stacks define a working surface for a tool. If small steelballs are used, conical structures or cones will form at the locationsof magnetic flux concentration through the balls. A coat of acrylicpaint is then applied to the elements and provides structural integrityto them. Prior to solidification of the paint, the cones may be shapedby passing a magnet near them. A magnet of opposite polarity from thepolarity of the base surface magnet will cause the cones to grow inheight; whereas, an identically poled magnet will cause the cones toflatten. This magnet may also be used to selectively orient the basesurface magnetic field which emanates from the protrusions to cause arealignment of the elements. This technique is used to produceasymmetrical cones which offer neutral or positive rake angle cuttingpoints on the working surface of the tool. After the cones have beenshaped and the paint has dried or solidified, a braze paste or fixingmeans consisting of a binder mixed with braze alloy is applied toencapsulate the cones and form a structural interconnection or flexiblesupport web or matrix between the cones. The paint maintains theintegrity of the cones and the braze paste provides a support web whichmaintains the cones in preselected positions on a flexible web beforebrazing and the braze alloy joins the cones in a solid structure orpattern after brazing. After the braze paste binder has dried orsolidified, the entire matrix may be removed from the base fixtureleaving the balls or other projections in place for further use. Theabrasive element matrix may the be cut to any desired shape. The releasemechanism may then be removed from the matrix and the matrix may besecured to another base structure such as a tool form having a smoothsurface by application of an acrylic adhesive. The acrylic adhesive maybe brushed on the matrix or the base structure or in the alternative maybe preinstalled and protected by a release liner. At this point, theassembly of matrix and base structure may be placed in a braze furnaceand heated to the necessary brazing temperature while maintaining acontrolled atmosphere such as hydrogen or a substantial vacuum. Afterthe brazing process has been completed, the assembly will feature a highfriction surface which may be used as an abrasive tool.

The advantages of the present invention are numerous. For one, themagnetic protrusions are secured to a reusable fixture. Consequently, itis not necessary to apply protrusions to the external surface of eachtool. Therefore, magnetic field resources may be applied to create anoptimum mosaic or pattern of protrusions which will then createrespectively positioned magnetic fields. A mosaic may be selected toaddress performance parameters ranging from material removaleffectiveness to surface finish quality. In addition, a substantialmanufacturing cost advantage may be realized by eliminating the materialcost of the balls as well as the labor associated with installing theballs on each tool.

Second, since the matrix is prepared on the generally planar surface ofthe fixture, which may be oriented in a horizontal plane, the carbideparticles are influenced by magnetic flux acting along a flux axisgenerally transverse to the mosaic surface and aligned withgravitational forces. Consequently the complications and irregularitiesthat are encountered when applying the particles directly to irregularlyshaped tools is eliminated.

In addition, the structure of the cones of the present invention may bealtered to produce a selectable rake angle (i.e., negative, neutral orpositive). That is, the present invention is suitable for preparation ofsymmetrical cones. These cones are prepared by using magnetic fluxhaving a flux axis which is generally perpendicular or normal to themosaic surface. If a neutral or positive rake angle is desired, conesmay be prepared by using a magnetic flux axis which is adjustable anddeterminable relative to the mosaic surface whereby the cone axis willhave a predetermined rake angle relative to the surface. For example, aneutral rake angle cone will be formed if the magnetic field is orientedsuch that the apex of the cone is located over a perpendicular drawn tothe base circular of the cone. A positive rake angle cone will be formedif the magnetic field is oriented so that the apex of the cone islocated outside of a perpendicular drawn to the base circle of the cone.In practice, the magnetic field may be selectively oriented by creatinga distortion above the surface of the fixture by use of a selectivelypositioned magnet or other ferromagnetic or electromagnet means.

The flexibility to produce cones having a selectable rake angleconstitutes a substantial performance advantage in that tools may beprepared to suit specific performance applications. That is, coneshaving a positive rake angle may be applied to tools used inapplications requiring aggressive material removal; whereas cones havinga neutral rake angle may be used for abrasive application requiring lessmaterial removal. Additionally, combinations of cone types may beapplied to the surface of a tool so that portions of the tool may beused for aggressive material removal and other portions may be used forproducing a desired surface finish. For example, the end or faceportions may be covered with cones having a negative rake angle toachieve a desired surface finish.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will beapparent to those skilled in the art to which the invention relates fromthe following detailed description of the invention made with referenceto the accompanying drawings in which:

FIG. 1 is a side view of the fixture used for preparing the firstembodiment of the present invention;

FIG. 2 is a cross sectional view of a portion of the fixture shown inFIG. 1 including a section of the cones prepared on the fixtureaccording to the first embodiment of the present invention;

FIG. 3 is a cross sectional view of a portion of a base structure havinga matrix prepared according to the first embodiment of the presentinvention applied thereto;

FIG. 3A is an enlarged section FIG. 3;

FIG. 4 is a cross sectional view of a portion of a base structure havinga matrix prepared according to the first embodiment of the presentinvention applied thereto;

FIG. 5 is an enlarged section of a base structure having a matrixprepared according to the first embodiment of the present inventionapplied thereto;

FIG. 6 is an enlarged section of another base structure having anothermatrix prepared according to the first embodiment of the presentinvention applied thereto;

FIG. 7 is a cross sectional view of a portion of an abrading toolprepared according to the first embodiment of the present invention;

FIG. 7A is an enlarged section of FIG. 7;

FIG. 8 is a cross section of a portion of a matrix prepared according tothe first embodiment of the present invention applied thereto;

FIG. 9 is a cross sectional view of a tool base with a portion of anabrading tool prepared according to the first embodiment of the presentinvention;

FIG. 10 is a cross sectional view of an abrading tool offering anegative rake angle to a workpiece.

FIG. 11 is a cross sectional view of an abrading tool offering a neutralrake angle to a workpiece;

FIG. 12 is a cross sectional view of an abrading tool offering apositive rake angle to a workpiece;

FIG. 13 is a side view with portions shown in cross section of a fixtureused to prepare a matrix having structures featuring neutral rakeangles;

FIG. 14 is a cross sectional view of the fixture including a matrixprepared according to the first embodiment of the present invention;

FIG. 15 is a cross sectional view of a portion of a base structurehaving a matrix prepared according to the first embodiment of thepresent invention applied thereto;

FIG. 16 is a cross sectional view of a portion of an abrading toolprepared according to the first embodiment of present invention;

FIG. 17 is a cross sectional view of the flat planar surface used forpreparing the second embodiment of the present invention;

FIG. 18 is a cross sectional view of the flat planar surface used forpreparing the second embodiment of the present invention exposed to amagnetic field and including an abrasive grit structure preparedthereon.

FIG. 19 is an enlarged section of FIG. 18;

FIG. 20 is a cross sectional view of a mold used for preparing the thirdembodiment of the present invention;

FIG. 21 is a cross sectional view of a matrix prepared according to thethird embodiment of the present invention;

FIG. 22 is a cross sectional view of an alternative mold for preparingthe third embodiment of the present invention;

FIG. 23 is a cross sectional view of a matrix prepared according to thethird embodiment of the present invention;

FIG. 24 is an illustration of a square cornered groove formed by thepresent invention:

FIG. 25 is a plan view of an offset centered pattern of abrasiveelements;

FIG. 26 is a side view of selected axes present in an offset centeredpattern of abrasive elements;

FIG. 27 is a plan view of a contact patch resulting from a tool engaginga workpiece;

FIG. 28 is a plan view of sequential patterns of abrasive elementsarranged on a tool;

FIG. 29 is a cross section of a wheel including the abrasive coating ofthe present invention arranged to produce a square cornered groove;

FIG. 30 is a side view of a fixture for use in preparing a matrixaccording to the present invention;

FIG. 31 is a plan view of flat arcuate segments A and B;

FIG. 32 is a cross sectional view of a flat sheet of matrix thermoformedover a curved die;

FIG. 33 is a side view of a semispheric or hemispheric like wheel coatedwith the matrix of the present invention; and

FIG. 34 is a plan view of a hemispheric-like wheel coated with thematrix of the present invention;

FIG. 35 is an enlarged plan view of a high friction surface having afine textured pattern on a first portion and a coarse textured patternon a second which in combination produce a herringbone pattern;

FIG. 36 is an enlarged plan view of a high friction surface havingcarbide structures with neutral rake angles on a first portion and asecond portion covered with carbide structures having a negative rakeangle; and

FIG. 37 is an enlarged plan view of a high friction surface prepared byplacing a pattern of carbide structures on selected portions and leavingother portions void.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The first embodiment of the present invention, as shown in FIG. 1,includes a fixture 10 comprising a permanent magnet 12 which is affixedto a first base structure or plate 14. Plate 14 provides a magnetic gapbetween magnet 12 and protrusions or steel balls 16. Consequently, thethickness of plate 14 is a parameter which may be adjusted until theideal magnetic field strength is achieved. Maximum magnetic fieldstrength is achieved if plate 14 is completely eliminated and magnet 14is placed in contact with protrusions 16. Alternatively, plate 14 may besuspended above magnet 12 to produce a selectively adjustable magneticfield by providing an adjustable height of suspension. Magnet 12 neednot be fixed to plate 14 and may be in the form of an electromagnet, orthe like.

A single layer of protrusions in the form of steel balls 16 are affixedby adhesive 20 to plate 14. Any ferrous or ferromagnetic structure maybe used in lieu of balls; for example, cylindrical steel rods may beused. Balls 16 may be arranged to provide a pattern in which sequentialrows of balls are arranged in an offset centered pattern, a straightcentered pattern or merely a shifted centered pattern or if desired arandom pattern. Release layer 18 may be a thin layer of a volatilizablematerial, a non-magnetic metal film, a low surface energy plasticcoating applied to balls 16, a low surface energy plastic film such asTeflon or a suitable mold release fluid such as silicone. A 5 mil layerof Teflon is used in the preferred embodiment. A source of vacuum may beintroduced to the region between the protrusions and release layer 18 byproviding suitable passageways (not shown). The vacuum will draw releaselayer 18 into firm contact with protrusions 16. This completes thefixture upon which a matrix of braze paste and magnetically orientedabrasive particles may be prepared.

Matrix 22, as shown in FIG. 3 is prepared by sprinkling or diffusing-200/+325 mesh tungsten carbide particles having a cobalt bindersintered thereto (not shown individually in this figure) onto releaselayer 18. The particles are attracted and collect on release layer 18 atthe locations of balls 16 as a result of the concentration of magneticflux produced by the balls acting on the magnetic field provided bymagnet 12. Abrasive particles used in the present embodiment exhibitproperties of a ferromagnetic body by the nature of the particlesthemselves or as a result of a ferromagnetic coating such as cobalt ornickel.

If a plurality of particles are deposited on a single point of magneticflux concentration, a conical collection of particles hereinafterreferred to as cones will form an abrasive structure 24 having an aspectratio which is a function of the applied magnetic field strength, theferromagnetic responsiveness of the particles, and other variable suchas agitation.

When the cones have reached a desired height by addition of particles,the cones are sprayed with an acrylic paint 31 (see FIG. 3A). While thepaint is still wet, cones 24 may be shaped by passing a second magnetover the upper surface of the fixture. A second magnet 40 oriented toexpose a pole opposite to that of magnet 12 is shown in FIG. 2. Anoppositely poled magnet will cause the cones to grow in height; whereas,a matching poled magnet will cause the cones to flatten. One skilled inthe art will recognize that second magnet 40 is utilized to enhance oralter the characteristics of magnet 12 and suitable conical structuresmay be produced without using second magnet 40. After the paint hasdried or solidified, the cones are coated with a water based brazecement (not shown) in FIG. 3 which is exaggerated which provides aprotective layer isolating the acrylic paint which protects thestructural integrity of the cones from the solvent contained in thecoating of interconnecting structure 26 which is added after the brazecement. A water based cement consisting of one part Nicrobraze CementType S, a trademark of Wall Colmonoy Corporation, and two parts water ispreferred. One skilled in the art will recognize that release layer 18may be removed from fixture 10 subsequent to drying of the paint toreduce station time of fixture 10. Interconnecting structure 26 is thenadded to encapsulate the cones. The interconnecting structure 26 mayconsist of a binder or cement, preferably 50 percent by weightNicrobraze Cement 1000, a trademark of Wall Colmonoy Corporation, and abraze alloy, preferably 50 percent by weight -325 mesh low melting pointbraze alloy. Any braze cement which dries or cures to provide a flexiblestructure will be satisfactory. Alternatively, various combinations andpermutations of ingredients including braze cement, braze alloys, andsetting material consisting of nonmelting particles may be used toprovide a structural interconnection of abrasive structures. Forexample, abrasive cone-like structures 24 may be interconnected by amixture of braze cement and nonmelting particles such as -325 mesh sizetungsten carbide particles or -325 mesh Wall Colmonoy Nicrogapparticles. Form 28 placed on release layer 18 serves as the outerboundary to which braze paste 26 will flow. The depth to which brazepaste 26 is applied or the height of form 28 will define the thicknessof the matrix.

Interconnecting structure 26 cures or dries to provide a flexible matrix22. This matrix 22 and release layer 18 may then be removed from fixture10 as a viable structural entity. Release layer 18 may then be removedfrom matrix 22 by peeling it away. Matrix 22 may be cut into desiredshapes at this point in time although cutting can also be done beforepeeling from the release layer.

Matrix 22 may then be secured to base structure 30, as shown in FIG. 3,by use of a thin film of acrylic pressure sensitive adhesive (notshown). The base structure may be any tool or other support. Anysuitable adhesive or binder which will vaporize and leave no residualash may be utilized. The adhesive may be applied directly to the matrixand a release liner may be used to protect the adhesive during storage.

Release layer 18 functions to provide a mechanism promoting separationof matrix 22 from protrusions 16. If a metal film or a low surfaceenergy plastic film is used, the respective film may be peeled awaybefore matrix 22 is installed on structure 30 as already described.Alternatively, the metal film may have a melting point such that if leftin place and brazed the metal film defines the interconnection betweenthe abrasive cone structures 24 and base structure 30. If avolatilizable material is used, the material may be left in place anddriven off by exposure to heat during the brazing process. If a moldrelease fluid or a low surface energy plastic coating is applied toprotrusions 16, the matrix may be removed from the fixture 10 andapplied directly to structure 30.

One skilled in the art may readily recognize that the release layer mayin fact be a substantially nonferromagnetic structure having a thinsection to which the abrasive structures are bonded as a result of abrazing operation or plating operation or through adhesion of theabrasive structures to the release layer by use of an appropriatebinder. Such a structure may be used as an abrasive device in the formof a flexible sand paper. Alternatively, the structure may be an objectsuch as a glove or boot which has portions coated to provide a highfriction surface.

FIG. 3A is an enlarged section of FIG. 3 illustrating matrix 22consisting of tungsten carbide particles 32 having a sintered cobaltbinder, acrylic paint 31 and interconnecting structure 26, whichpreferably consists of braze alloy 34 and cement 36. After matrix 22 hasbeen secured to the surface of base structure 30, the entire assemblymay be placed in a braze furnace and heated to brazing conditions, thatis, the necessary brazing temperature for the necessary time period. Anytemperature between 1850° F. and 2050° F. for a time period ofapproximately 15 minutes is appropriate for a low melting point brazealloy. An atmosphere of pure dry hydrogen or a vacuum is recommended. Ahold of 30 minutes is recommended at 800° F. before elevating to brazetemperature. At braze temperature, braze alloy 34 will become molten andflow to form a mortar-like bond of metal 38 (as shown in FIG. 7A) whichsecures or joins the tungsten carbide particles 32 together individuallyand to the base structure 30. Thus, after brazing, only the braze alloyremains as all paints and binders have vaporized.

One skilled in the art will readily recognize that if interconnectingstructure 26 consists of a layer of resin or a layer of braze cement andsetting material and the coated cone structures 24 already havestructural integrity, a braze alloy must be cast thereupon as asubsequent layer of braze alloy and cement either before or after matrix22 has been secured to a tool surface.

Alternatively, matrix 22 may be prepared by including a braze alloy 34within the abrasive cone structures 24 among the abrasive particles 32(as shown in FIG. 5). The interconnecting structure 26 may be formed ofa vaporizable cement 36. Such a matrix 22 may be removed from fixture 10and applied to base structure 30 for a subsequent brazing operation aspreviously described.

Alternatively, matrix 22 may be prepared using abrasive particles 32which have been coated with a braze alloy 34 in an acrylic binder 31 asshown in FIG. 6. The interconnecting structure 26 is formed of avaporizable cement 36. Such a matrix 22 may be removed from fixture 10and applied to a base structure 30 for a subsequent brazing operation aspreviously described.

Alternatively, matrix 22 may be prepared using abrasive particles 32which are heated such that only a surface portion becomes molten andbonds to immediately surrounding particles and structures to formabrasive cone-like structures 24. FIG. 6 illustrates such a phenomena asportion 34 becomes molten so as to bond the remainder of particle 32 asdescribed. Such a matrix 22 includes a vaporizable cement 36 to definethe structural interconnection between abrasive structures 24. Such amatrix 22 formed on fixture 10 may be transferred to a base structure 30for a subsequent sintering operation. While throughout this descriptionthe term "cone-like structures" has been used, it should be recognizedthat is a broad term including ridges, pyramids, or other patterns.

Alternatively, matrix 22 may be prepared using a cement 36 tointerconnect abrasive structures 24, as shown in FIG. 8, for subsequentsecurement to base structure 30 by a plating operation, as shown in FIG.9. Those skilled in the art will recognize that numerous techniques maybe utilized to define the structural interconnection of particles 32 tothe base structure 30 including IN-SITU application of a braze pastcomprising braze alloy 34 and cement 36, as shown in FIG. 4 after thismatrix is placed on base 30.

The final product, as shown in FIG. 7, is a base structure 30 which isarmed with cone-like structures 24 B which provide the abrading toolcutting points. The base structure may be a cylindrical shape (such as agrinding wheel or an end mill), a flat rectangular shape (such as a handfile), or a long thin shape (such as a saw blade). Base structures whichinclude a compound curve may be coated with an otherwise flat matrix 22by trimming the matrix using known techniques to develop the respectiveshape from a flat sheet and alternatively the matrix may be thermoformedto a desired shape. Such a situation may be presented when trying tocover semicircular wheel 610 shown in FIG. 33 using the technique shownin FIGS. 31-34. Arcuate segments A,B formed of flat sheets may be usedto proximate the spherical shape if several segments are used. Athermoforming operation may reduce the number of segments required.Thermoforming may be completed by exposing the flat sheets, A, B to aheat lamp or heated air supplied by a heat gun while the arcuatesegments are situated on a die 612 as shown in FIG. 32 featuring aproperly shaped profile. The matrix of one preferred embodiment of thepresent invention incorporates a thermoformable resin which becomesplastic upon heating and may then be formed into a desired shape whichis retained upon subsequent cooling. Application of a thermoformedmatrix such as A,B is accomplished in an identical manner to thatpreviously described.

A symmetrical cone 46 shown in FIG. 10 will present a negative rakeangle X with respect to workpiece 48 and base structure 30. A negativerake angle is preferred in abrasive applications in which low-ratematerial removal is specified. A symmetrical cone 46 may be produced bythe fixture previously described. FIG. 11 illustrates an asymmetric cone46' having a neutral rake angle Y. A neutral rake angle is preferred inmoderate-rate material removal applications. FIG. 12 illustrates anotherasymmetric cone 46" having a positive rake angle Z. A positive rakeangle Z is preferred in aggressive-rate material removal applications.

These asymmetric cones may be generated by using the fixture shown inFIG. 13. Fixture 52 comprises a permanent magnet 12, secured to plate14, having steel balls 16 secured thereto. Release layer 18 is thenplaced over balls 16. Carbide particles (not shown individually in thisfigure) are then sprinkled through diffuser 56 onto release layer 18 toform cones 24 having generally symmetrical shapes (See portion I). Themagnetic flux emanating from the steel balls located in portion II isdistorted by the presence of second magnet 40" such that the lines offlux in portion II are no longer emanating perpendicular to the surface.Other techniques to reorient the magnetic lines of flux such as theorientation of the magnetic flux source or placement of a ferromagneticobject above the surface of steel balls 16 may be used. Consequently,the cones located in portion II will align themselves with thereoriented lines of flux. The individual cone shown in portion II has aneutral rake angle. A positive rake angle is formed by locating magnet40" farther to the right (in relation to this figure) from portion II.Acrylic paint is applied to cones 24 located in portion II by applicator54. Once the paint has dried or solidified, the cones will maintain theorientation produced by the distorted lines of flux. The cones locatedin portion III are ready to be encapsulated with braze paste (not shown)as described previously. In actual operation, magnet 40", paintapplication mechanism 54 and diffuser 56 will move with respect tofixture 52 and thus prepare a continuous matrix of magnetically orientedcarbide particles and braze paste.

FIG. 35 shows an abrasive surface prepared with a fine textured matrixof structures on a first half portion 100 and a coarse textured matrixon the second half portion 102. In addition, the individual matricesprovide a herringbone pattern which facilitates conveyance of chips toeach side as the abrasive surface is advanced relative to a workpiece inthe direction of the arrow shown. The coarse and fine textured matricesare produced by selecting ball sizes which will produce the desiredspacing between the individual carbide structures. The herringbonepattern is produced by a specific arrangement of balls on the fixturepreviously described and shown in FIG. 1.

FIG. 36 shows an abrasive surface prepared with a negative rake anglematrix placed on a first portion 104 and a neutral rake angle matrixplaced on a second portion 106. The apex 105 of the conical structuresin illustrated as a dot and the respective base circle 107 of thestructures is shown as a circle. Such a technique may be utilized tocreate an abrasive wheel which may be used to cut and finish aworkpiece. That is, a more aggressive rake angle cone (i.e., a conehaving a neutral rake angle) may be used on the first portion advancedinto the workpiece and a less aggressive rake angle cone (i.e., a conehaving a negative rake angle) may be used on the second trailing portionto finish the surface of the workpiece. Thus in one advance of theabrasive wheel, two operations may be performed.

FIG. 37 shows an abrasive surface prepared having portions 108 thereofcovered by a matrix and portions 110 left void to offer passagewaysfacilitating the elimination of scrap from the tool/workpiece interface.An identical abrasive surface may be prepared by leaving out rows ofprotrusions on the fixture. That is, the matrix may be prepared as acontinuous structure wherein selected rows of small steel balls 16 (asshown in FIG. 1) may be left void thereby producing passagewaysfacilitating the elimination of scrap from the tool/workpiece interface.This eliminates the necessity to cut and patch together portions of thematrix to produce the voids.

One skilled in the art will recognize that a matrix 722 including amonolayer of abrasive particles 724, as shown in FIG. 14, may beprepared by distributing abrasive particles 724 on the base structure orplate 714 of fixture 710; featuring magnetic flux concentrationsproduced by balls 716 and magnet 712. Particles 724 come to rest onrelease coating 718 at the points of magnetic flux concentration andalign with major axes parallel with the path of magnetic flux. Astructural interconnection is prepared by casting a first layer of brazepaste 726 and a subsequent layer of setting material 727 saturated witha hydrocarbon resin. Setting material used in the present embodimentpreferably includes a non-melting particle smaller in size than abrasiveparticle 724. Such a structure may be transferred to a tool surface 730shown in FIG. 15 with the planar surface defined by release layer 718maintained as the outer peripheral surface 725. FIG. 15 is an enlargedview of the matrix including a layer of braze paste 726 including brazealloy 734 and braze cement 736 and a layer of setting material 727 onbase structure 730. Subsequent to brazing to a tool surface 30 as shownin FIG. 16, setting material 727 which has been infiltrated by brazealloy 734, acts as a shim and maintains proper height of the respectiveabrasive particles such that a planar relation is maintained. Further,the casting process described herein is one technique to provide an evendistribution of braze alloy or setting material. Other techniques suchas distributing particles of braze alloy and/or setting material in dryform and then saturating same with a hydrocarbon resin may accomplishthe same with a hydrocarbon resin may accomplish the same objective.

Another embodiment of the present invention, as shown in FIG. 17,utilizes a flat planar nonferromagnetic support 214 including releaselayer 218, as previously described. A monolayer of ferromagneticelements 216 is distributed either randomly or by mechanical positioningtechniques or by distributing particles on a fixture defining magneticflux concentrations as described in relation to the other embodiments ofthe present invention. Subsequent to distribution of ferromagneticelements 216, a layer of resin 220 is applied to maintain theinterpositional relation thereof. Next, a magnet 212, as shown in FIG.18, is introduced to provide a magnetic field proximate support 214.Ferromagnetic elements 216 produce magnetic flux axes therethrough whichfunction to collect subsequently applied abrasive particles (not shownindividually) which are distributed in the manner previously describedwith respect to the first embodiment. Abrasive particles used in thepresent embodiment exhibit properties of a ferromagnetic body by thenature of the particles themselves or as a result of a ferromagneticcoating such as cobalt or nickel. In this embodiment of the presentinvention such particles collect to form conical structures 224 at thelocations of magnetic flux formed by ferromagnetic elements 216. Next,an interconnecting structure 226 is formed to provide structuralintegrity to matrix 222. The interconnecting structure includes brazealloy 234 and braze cement 236 (as shown in FIG. 19). The release layer,transfer techniques and methods of providing structural interconnectionas described in relation to the first embodiment of the presentinvention may be utilized to apply the respectively produced abrasivegrit structure to the surface of tool base 230. In addition, the rakeangle of conical structures 224 presented to the workpiece is subject tothe orientation of the magnetic field passing therethough and as suchmay be altered according to the principles defined in the firstembodiment of the present invention. Although discrete ferromagneticparticles are shown providing loci of magnetic flux concentration, theconcept of the second embodiment of the present invention can beaccomplished using other known techniques to secure ferromagneticelements to the release layer, such as applying collections of cobalt orferrite powder and resin on the release layer using known printingtechniques.

In still another embodiment, the abrasive structures 324 are prepared byuse of a mold 314 having a plurality of concave indentations 315 asshown in FIG. 20. The indentations formed in the mold may be any shapewhich will provide a receptacle for a single abrasive particle or aplurality of abrasive particles. The indentations may be arranged toprovide a pattern in which sequential rows of abrasive elements arearranged in an offset centered pattern, a straight centered pattern ormerely a shifted centered pattern or, if desired, a random pattern. Inthe examples shown in FIG. 20, abrasive structures 324 includes aplurality of abrasive particles (not shown individually) bound togetherby resin (not shown). However, in the alternative, a single abrasiveparticle may be placed in the indentation and surrounded and supportedby setting material. Setting material used in the present embodiment ispreferably a nonmelting particle smaller in size than the respectiveabrasive particle. As shown in FIG. 21, the abrasive structure 324 isreleased from mold 314 and deposited on a flat planar surface 316covered by release layer 318. The plurality of abrasive structures 324may be maintained in respective positions on layer 318 by application ofa light magnetic flux, vacuum, registration with indentations, orregistration with respective magnetic flux concentrations.Alternatively, the abrasive structures 324 may be maintained inrespective positions defined by mold 314 by use of a light coat of resinapplied to release layer 318, leaving the release is layer tacky priorto deposition of abrasive structures 324 thereon. Referring back to FIG.20, a structural interconnection may also be realized by use of asubstrate layer interconnecting the abrasive structures comprised ofresin or resin and nonmelting particles or resin and a braze alloy. Thesubstrate layer may be created by filling mold 314 beyond the depth ofindentations 315 up to dike 328.

One skilled in the art will readily recognize that the techniques tomaintain the interpositional relationship of abrasive structures 324 areintended to maintain the respective abrasive elements in fixed positionsas established in the mold 314 in FIG. 20. This position maintenance istemporary while subsequent operations are performed which define a morepermanent interpositional relationship therebetween. Referring again toFIG. 21, next, an interconnecting structure 326 may be formed to providestructural integrity to matrix 322. In the preferred embodiment theinterconnecting structure 326 includes braze alloy 334 and braze cement336. Subsequent to release from layer 318 and installation on a basetool structure, the assembly is heated to braze conditions whereuponbraze alloy 334 infiltrates abrasive structures 324 to form a bondtherebetween and to said tool surface. The release layer, transfertechniques and methods of providing structural interconnection asdescribed in relation to the first embodiment of the present inventionmay be utilized to apply the respectively produced abrasive gritstructures to a tool surface.

Alternatively, mold 814 as shown in FIG. 22 may be constructed from avolatilizable material. Examples include a mold formed of a film ofpolyester resin or a fluorocarbon which has been vacuum formed toprovide indentations 815 for receipt of abrasive particles to formabrasive structures 824. As such, abrasive structures 824 may bemaintained in the mold by application of a water based binder whileinterconnecting structure 826 is formed thereon as shown in FIG. 23. Inthe alternative, interconnecting structure 826 which is partiallyprovided for by mold 814 may be accomplished by utilizing the manyconcepts previously described with respect to the first embodiment forattachment to a base structure 830. For example, braze alloy may beincluded among the carbide particles of the abrasive elements 824.Alternatively carbide particles may be utilized which are coated withbraze alloy or the abrasive particles may be sintered in place. Also,the abrasive particles may be plated in place. Finally, braze paste maybe applied after mold 814 with abrasive elements 824 still in place hasbeen secured to a tool base 830.

The matrices 322 and 822 prepared according to the techniquesillustrated in FIG. 20 through 23 may be placed in a magnetic fieldcausing abrasive elements 324 or 824 to act as magnetic fluxconcentrators. At such time additional abrasive particles may be addedto the apex of such structures to enhance the cutting properties or lifeof abrasive structures 324 or 824. Examples of such abrasive particlesmay include nickel coated diamond particles or tungsten carbideparticles having a cobalt binder imparting ferromagnetic propertiesthereto. Alternatively, such particles may be applied IN-SITU by firstsecuring matrix 322 or 822 to a base tool structure 830 and magnetizingsame.

The texture or relative coarseness which is presented to a workpiece bya tool incorporating the abrasive elements of the various embodiments ofthe present invention is a function of the spacing of the individualabrasive elements and the interpositional relationships therebetween. Inpractice, an optimization is sought to maximize the coarseness of theabrasive tool while continuing to achieve a given surface finishspecification. Such an optimization will maximize tool life andproductivity while reducing heating of the workpiece. One technique toaccomplish such an objective is presented by Keeleric in U.S. Pat. No.2,820,746. According to Keeleric, each abrasive element is displacedfrom the preceding element so that the path of each element through theworkpiece does not overlap that of one or more preceding elements. Sucha technique may be accomplished in the embodiments of this invention bycreating a pattern of abrasive elements which are arranged in sequentialrows having offset centers which may repeat from time to time. Such anoffset centered pattern includes various axes along which sequentiallypositioned abrasive elements align themselves. These axes may beobserved in side profile by moving to the various positions 0°, 10°,30°, 50°, 60°, 70° and 90° or other similarly related angles as shown inFIG. 26. A variety of results may be accomplished by controlling theorientation of such a pattern with respect to the axis of relativemotion between the pattern and the workpiece such axis of relativemotion comprising the "workpiece path" or "path". For example, with theparticular equilateral triangle pattern of abrasive elements shown inFIG. 25, if the 30° of 90° axes are aligned with the axis of relativemotion, maximum material removal and maximum surface roughness will berealized. However, if another angle such as the 10°, 50° of 70° axes isaligned with the axis of relative motion, minimum material removal andmaximum surface smoothness will be achieved.

It may be observed that if the pattern of FIG. 25 is laid on either anannular or peripheral, i.e., cylindrical, surface of a rotatable mounteddisc, the 10 and 70 degree axes repeat as one moves about the patternannular or periphery. Such repetition will continue about a center 910in the II, III, and IV quadrants of the pattern (not shown). Mostapplications will benefit from selection of a coarse texture which hasbeen oriented in proximate alignment with for example the 10° axis.Improvements in surface finish may be realized by using any variation inthe range of 5 degrees thereabout. An ideal finish will be produced byusing a first pattern with the path oriented at 5 to 15 degrees in afirst portion of the finished tool followed by a second portion with apattern oriented in the opposing direction relative to the path (i.e.,-5 to 15 degrees). Such an alternative orientation produces analternating sidewise sweeping motion not available if a random orconsistent pattern is used.

When an offset centered pattern of abrasive elements is used to abrade amaterial having elasticity (such as rubber), stresses are imposed on theworkpiece in the form of tension and compression (as shown in FIG. 27).In addition, any cant of such a pattern with respect to the axis ofrelative motion causes lateral stresses in the form of tension andcompression. As shown in FIG. 27, if a pattern of abrasive elements 412of a tool engaging a workpiece 414 is arranged in an offset centeredpattern and canted with respect to the axis of relative motion of thetool indicated by arrow 411, that is, the path of the relative motion ofthe tool and the workpiece, a sideward thrust will be imparted toworkpiece 414 resulting in compression 416 and tension 418. The sidethrust is in addition to the normal compression 420 and tension 422imposed by contact therebetween. Compression 416, 420 and tension 418,422 which exist during the abrading process cause deformation of theworkpiece which can result in removal of material which has beendeformed out of position such that upon relief of the respective tensionand compression the final unstressed dimensions are not identical to thedimension produced by the abrading process. Altering the cant ofsequential first pattern 424, the first portion of the tool shown inFIG. 28 and the second portion with pattern 426 and/or interrupting thepattern by introducing discontinuities, as shown in the lower portion ofFIG. 28, results in shifting of stress locations and intermittent reliefof stresses. Interspersing patterns 428 in selected portions of the toolarranged with a major axis aligned with the axis of relative motion 430will enhance the material removal rate while patterns 424 and 426 willprovide for surface smoothness. To assure that the final dimensions ofthe workpiece in an unstressed condition is equal to the dimensions ofthe workpiece produced by the abrading process combinations andpermutations of patterns may be sequentially arranged about thecircumference of a wheel.

Utilizing this concept of preferential orientation of the patterns ofabrasive elements, a grooving wheel may be prepared which producesrecess 511 with a square corner in workpiece 510 for example as shown inFIG. 24. The wheel 512 (as shown in FIG. 29) is produced by coating thecircumference of the wheel with abrasive elements 513 having elementaxes which are arranged generally coplanar with each face 514,516 ofwheel 512. The abrasive elements are produced in the manner previouslydescribed for generating neutral rake angle cones (see FIG. 11). Amatrix produced using these previously described techniques may be cutalong a line of cones and placed on the circumference of the wheel andaligned with the edge thereof. A portion of the circumference may becoated with a matrix as described and the remaining portion may becoated with cones oriented in the opposite direction as shown in FIG.30. A smooth finish is produced by coating a portion of thecircumference with a matrix oriented as previously described with theoffset centered axis canted ±5 to 15° from the axis of relative motionwith the workpiece. Alternatively, the cones in a single section of amatrix may be oriented to align with each edge while at the same timeaccomplishing the finishing objective of the present invention. Such amatrix could be prepared by utilizing a fixture as previously describedand proportioned as per the illustration of FIG. 30.

It is further thought that the apparatus and method of the presentinvention and many of its intended advantages will be understood fromthe foregoing description and it will be apparent that various changesmay be made in form, construction and arrangement of parts thereofwithout departing from the spirit and scope of the invention orsacrificing all of its material advantages; the form herein beforedescribing being merely a preferred or exemplary embodiment.

What is claimed is:
 1. An abrasive tool for removing material from aworkpiece by contact and relative motion between a working surface ofsaid tool and the workpiece, said tool comprising:a cylindrical basehaving a central axis about which it can be rotated and a cylindricalbase surface, said base surface including a plurality of workingsegments; and a collection of particles forming a plurality of abrasiveelements disposed on one of said segments and arranged in a pattern ofarcuate rows having a first pattern axis, adjacent elements in each rowof said one segment being spaced apart and adjacent rows of said onesegment being spaced apart, the spacing between adjacent rows beinguniform and the spacing between adjacent elements of a row beinguniform, said first pattern axis being offset at a small acute anglerelative to said central axis.
 2. The abrasive tool of claim 1 whereinsaid offset is no greater than 15 degrees.
 3. The abrasive tool of claim1 wherein said offset is between 5 and 15 degrees.
 4. The abrasive toolof claim 1 including a second segment having abrasive elements in saidpattern of arcuate rows and having a second pattern axis with no offsetrelative to said central axis.
 5. The abrasive tool of claim 1 whereinsaid abrasive elements have an element axis and a distal workingportion, said distal working portion defining the working surface, saidelements comprising:a plurality of particles disposed in a stackedconfiguration on said cylindrical base surface with an apex at saidworking surface and a braze alloy fusing said particles to said basesurface to define said stacked configuration.
 6. The abrasive tool ofclaim 5 wherein said particles are magnetically responsive.
 7. Theabrasive tool of claim 6 wherein said particles are coated with cobalt.8. The abrasive tool of claim 1 wherein said particles are rigidlyinterconnected and secured to said base surface by a fused brazingalloy.
 9. The abrasive tool of claim 8 wherein said particles have asize in the range of about -200 to +325 mesh.
 10. An abrasive tool forremoving material from a workpiece by contact and relative motionbetween a working surface of said tool and the workpiece, said toolcomprising:a cylindrical base having a central axis about which it canbe rotated and a cylindrical base surface, said base surface including aplurality of working segments; a collection of particles forming aplurality of abrasive elements disposed on one of said segments andarranged in a pattern of arcuate rows having a first pattern axis,adjacent elements in each row of said one segment being spaced apart andadjacent rows of said one segment being spaced apart, the spacingbetween adjacent rows being uniform and the spacing between adjacentelements of a row being uniform, said first pattern axis being offset ata small acute angle relative to said central axis; a collection ofparticles forming a plurality of abrasive elements disposed on a secondsegment and arranged in a pattern of arcuate rows having a secondpattern axis, adjacent elements in each row of said second segment beingspaced apart and adjacent rows of said second segment being spacedapart, the spacing between adjacent rows being uniform and the spacingbetween adjacent elements of a row being uniform, said second patternaxis being offset at a small acute angle relative to said central axisin the direction opposite the offset of said first pattern axis.
 11. Theabrasive tool of claim 10 wherein the offsets of said first and saidsecond pattern axes from said central axis are no greater than 15degrees.
 12. The abrasive tool of claim 11 wherein the offsets arebetween 5 and 15 degrees.
 13. The abrasive tool of claim 10 including athird segment having said pattern of arcuate rows having a third patternaxis, the pattern axis of said third segment being offset by, about 10degrees from said central axis.
 14. The abrasive tool of claim 13wherein the offset of said first segment is up to about 5 degrees fromsaid third pattern axis toward said central axis and the offset of saidsecond segment is up to about 5 degrees from said third pattern axisaway from said central axis.
 15. The abrasive tool of claim 5 whereinsaid abrasive elements are in the configuration of circular cones. 16.An abrasive tool for removing material from a workpiece by contact andrelative motion in a working direction between a working surface of saidtool and the workpiece, said tool comprising:first and second adjacent,contiguous and integral cylindrical bases, each base having a centralaxis and a cylindrical base surface, each base surface including aplurality of working segments; a collection of particles forming aplurality of abrasive elements disposed on one of said segments andarranged in a pattern of arcuate rows having a first pattern axis,adjacent elements in each row of said one segment being spaced apart andadjacent rows of said one segment being spaced apart, the spacingbetween adjacent rows being uniform and the spacing between adjacentelements of a row being uniform, said first pattern axis being offset ata small acute angle relative to said central axis; a collection ofparticles forming a plurality of abrasive elements disposed on a secondsegment and arranged in a pattern of arcuate rows having a secondpattern axis, adjacent elements in each row of said second segment beingspaced apart, the spacing between adjacent rows being uniform and thespacing between adjacent elements of a row being uniform, said secondpattern axis being offset at a small acute angle relative to saidcentral axis in the direction opposite the offset of said first patternaxis; the central axis on the first cylindrical base being offset by anangle of about 30° relative to said working direction and the centralaxis of said second cylindrical base being aligned in said workingdirection, the first and second pattern axes of the second cylindricalbase being offset by an angle between about 5° and 15° from the centralaxis of said second base.
 17. An abrasive tool for removing materialfrom a workpiece by contact and relative motion between a workingsurface of said tool and the workpiece, said tool comprising:a basehaving a working direction and a base surface, said working directiondefining a direction of relative motion of the workpiece and saidworking surface for removal of material from said workpiece, said basesurface including a plurality of working segments aligned in saidworking direction; a collection of particles forming a plurality ofabrasive elements disposed on one of said segments and arranged in apattern of rows having a first pattern direction, adjacent elements ineach row of said one segment being spaced apart and adjacent rows ofsaid one segment being spaced apart, the spacing between adjacent rowsbeing uniform and the spacing between adjacent elements of a row beinguniform, said first pattern direction being offset at a small acuteangle relative to said working direction; and a collection of particlesforming a plurality of abrasive elements disposed on a second segmentand arranged in a pattern of rows having a second pattern direction,adjacent elements in each row of said second segment being spaced apartand adjacent rows of said second segment being spaced apart, the spacingbetween adjacent rows being uniform and the spacing between adjacentelements of a row being uniform, said second pattern direction being ata small acute angle relative to said working direction offset in thedirection opposite the offset of said first pattern direction.
 18. Anabrasive tool for removing material from a workpiece by contact andrelative motion between a working surface of said tool and theworkpiece, said tool comprising:a base having a working direction and abase surface, said working direction defining a direction of relativemotion of the workpiece and said working surface for removal of materialfrom said workpiece, said base surface including a plurality of workingsegments aligned in said working direction; a collection of particlesforming a plurality of abrasive elements disposed on one of saidsegments and arranged in a pattern of rows having a first patterndirection, adjacent elements in each row of said one segment beingspaced apart and adjacent rows of said one segment being spaced apart,the spacing between adjacent rows being uniform and the spacing betweenadjacent elements of a row being uniform, said first pattern directionbeing aligned with said working direction; a collection of particlesforming a plurality of abrasive elements disposed on a second segmentand arranged in a pattern of rows having a second pattern direction,adjacent elements in each row of said second segment being spaced apartand adjacent rows of said second segment being spaced apart, the spacingbetween adjacent rows being uniform and the spacing between adjacentelements of a row being uniform, said second pattern direction offset ata small negative acute angle relative to said first pattern direction;and a plurality of abrasive elements disposed on a third segment andarranged in a pattern of rows having a third pattern direction, adjacentelements in each row of said third segment being spaced apart andadjacent rows of said third segment being spaced apart, the spacingbetween adjacent rows being uniform and the spacing between adjacentelements of a row being uniform, said third pattern direction beingoffset at a small positive acute angle relative to the first patterndirection.
 19. The abrasive tool of claim 18 wherein said offsets are nogreater than 15 degrees.
 20. The abrasive tool of claim 18 wherein saidoffsets are between 5 and 15 degrees.
 21. The abrasive tool of claim 18wherein said working surface is flat.
 22. The abrasive tool of claim 18wherein said abrasive tool is rotatable about a central axis and saidworking surface is a radially extending annulus.
 23. The abrasive toolof claim 18 wherein an element in one row of elements is intermediatetwo adjacent elements of an adjacent row to define a triangle.
 24. Theabrasive tool of claim 18 wherein the adjacent elements in two adjacentrows of a pattern are rectilinearly oriented.
 25. An abrasive tool forremoving material from a workpiece by contact and relative motionbetween a working surface of said tool and the workpiece, said toolcomprising:a base having a working direction and a base surface, saidworking direction defining a direction of relative motion of theworkpiece and said working surface for removal of material from saidworkpiece, said base surface including a plurality of working segmentsaligned in said working direction; a collection of particles forming aplurality of abrasive elements disposed on one of said segments andarranged in a pattern of rows having a first pattern direction, adjacentelements in each row of said one segment being spaced apart and adjacentrows of said one segment being spaced apart, the spacing betweenadjacent rows being uniform and the spacing between adjacent elements ofa row being uniform, said first pattern direction being aligned withsaid working direction; a collection of particles forming a plurality ofabrasive elements disposed on a second segment and arranged in a patternof rows having a second pattern direction, adjacent elements in each rowof said second segment being spaced apart and adjacent rows of saidsecond segment being spaced apart, the spacing between adjacent rowsbeing uniform and the spacing between adjacent elements of a row beinguniform, said second pattern direction offset at a small negative acuteangle relative to said first pattern direction; and a plurality ofabrasive elements disposed on a third segment and arranged in a patternof rows having a third pattern direction, adjacent elements in each rowof said third segment being spaced apart and adjacent rows of said thirdsegment being spaced apart, the spacing between adjacent rows beinguniform and the spacing between adjacent elements of a row beinguniform, said third pattern direction being offset at a small positiveacute angle relative to the first pattern direction; wherein, in one ofsaid segments, an element in one row of elements is intermediate twoadjacent elements of an adjacent row oriented so that a line connectingsaid element in said one row and either element in said adjacent rowdefines a 30 degree angle with the pattern direction.
 26. An abrasivetool for removing material from a workpiece by contact and relativemotion between a working surface of said tool and the workpiece, saidtool comprising:a base having a working direction and a base surface,said working direction defining the direction of relative motion of theworkpiece and said working surface for removal of material from saidworkpiece, said working surface including a plurality of workingsegments aligned in said working direction; and a collection ofparticles forming a plurality of abrasive elements disposed on one ofsaid segments and arranged in a pattern of rows having a first patterndirection, adjacent elements in each row of said one segment beingspaced apart and adjacent rows of said one segment being spaced apart,the spacing between adjacent rows being uniform and the spacing betweenadjacent elements of a row being uniform, said first pattern directionbeing offset relative to said working direction.
 27. An abrasive toolfor removing material from a workpiece by contact and relative motionbetween said tool and workpiece, said tool comprising:a cylindrical basehaving a central axis about which it can be rotated and a cylindricalworking surface, said working surface including a plurality of workingsegments; and a collection of particles forming a plurality of abrasiveelements disposed on one of said segments and arranged in a pattern ofarcuate rows, adjacent elements in each row of said one segment beingspaced apart and adjacent rows of said one segment being spaced apart,the spacing between adjacent rows being uniform and the spacing betweenadjacent elements of a row being uniform, said arcuate rows definingfirst pattern planes which intersect a plane normal to said central axisat a small acute angle.
 28. The abrasive tool of claim 27 wherein saidacute angle is no greater than 15 degrees.
 29. The abrasive tool ofclaim 27 wherein said acute angle is between 5 and 15 degrees.
 30. Theabrasive tool of claim 27 having a second segment having said pattern ofarcuate rows defining second pattern planes which have a parallelorientation relative to a plane normal to said central axis.
 31. Anabrasive tool for removing material from a workpiece at two axiallyspaced stages by contact and relative motion between working surfaces ofthe tool and the workpiece, said tool comprising:a cylindrical basehaving a central axis about which it can be rotated and first and secondadjacent and contiguous cylindrical base surfaces; a collection ofparticles forming a plurality of abrasive elements disposed on saidfirst base surface and said second base surface and arranged in apattern of arcuate rows having a pattern axis, adjacent elements in eachrow being spaced apart and adjacent rows being spaced apart, the spacingbetween adjacent rows being uniform and the spacing between adjacentelements of a row being uniform, each of said abrasive elements havingan element axis and a distal working portion defining the workingsurface, each of said elements comprising a plurality of particlesdisposed in a stacked configuration on said cylindrical base surfaceswith an apex at said working surface and a braze alloy fusing saidparticles to said base surface to define said stacked configuration; theparticle size element size, element spacing, and pattern axis of theelements on said first base surface selected to provide a relativelyaggressive first working surface and the particle size, element size,element spacing, and pattern axis of the elements on said second basesurface selected to provide a relatively fine second working surface.32. The abrasive tool of claim 31 wherein the elements on said firstbase surface are larger than the elements on said second base surface.33. The abrasive tool of claim 31 wherein the elements on said firstbase surface are more widely spaced than the elements on said secondbase surface.
 34. The abrasive tool of claim 31 wherein the elements onsaid first base surface are made up of larger particles than theelements on said second base surface.
 35. The abrasive tool of claim 31wherein the pattern axis of said rows of elements on said first basesurface is closer to said central axis than the pattern axis of rows ofelements on said second base surface.
 36. An abrasive tool for removingmaterial from a workpiece by contact and relative motion between aworking surface of said tool and the workpiece, said tool comprising:abase having a central axis, a working direction and a base surface, saidworking direction defining a direction of relative motion of theworkpiece and said working surface for removal of material from saidworkpiece, said base surface including first and second working segmentson opposite sides of said central axis;a collection of particles forminga plurality of abrasive elements disposed on said first segment andarranged in a pattern of rows having a first pattern direction, adjacentelements in each row of said one segment being spaced apart and adjacentrows of said one segment being spaced apart, the spacing betweenadjacent rows being uniform and the spacing between adjacent elements ofa row being uniform, said first pattern direction being offset at asmall acute angle relative to said central axis; and a collection ofparticles forming a plurality of abrasive elements disposed on saidsecond segment and arranged in a pattern of rows having a second patterndirection, adjacent elements in each row of said second segment beingspaced apart and adjacent rows of said second segment being spacedapart, the spacing between adjacent rows being uniform and the spacingbetween adjacent elements of a row being uniform, said second patterndirection being at a small acute angle relative to said central axisoffset in the direction opposite the offset of said first patterndirection.
 37. The abrasive tool of claim 36 wherein the central axis isaligned with said working direction.
 38. The abrasive tool of claim 36wherein the central axis forms a 30° angle with said working direction.39. The abrasive tool of claim 36 wherein the small acute angles arebetween about 5° and 15°.
 40. The abrasive tool of claim 38 wherein thesmall acute angles are between about 5° and 15°.